Rewrite as a simplified fraction. ${1.76\overline{2} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1762.2222...\\ 100x &= 176.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1586}$ ${x = \dfrac{1586}{900}} $ ${x = \dfrac{793}{450}} \text{or} {1 \dfrac{343}{450}}$